Translucent vinyl plastic material
This is the setup I use for glasses, producing results such as the one above. It works by rendering the material as regular glass, except for lightrays that bounce too much (that is, more than three times), in which case it gets rendered as a simple green, transparent material. The Volume Absorption node is there to make sure the effect still happens when the sheet of glass is viewed from the side.

You can adjust it to your own needs by substituting the Glass BSDF node for the one(s) you've so far been using and tweaking the colours to your liking.



You can check this and many other tricks for rendering glass-like materials in Vilem Duha's Blender conference, Everything you wanted to know about rendering Glass not only with Cycles.